Apparently the two look similar: both occur primarily online, and both focus on creating digital content for people to consume. So what's the difference?
The term “digital marketing” does not differentiate between “inbound” and “outbound” marketing tactics. Both fit within the term digital marketing.
Outbound tactics aim to put a marketing message in front of as many people as possible in the online space – regardless of its relevance to that audience. For example, the flashy banner ads you see at the top of many sites talking about a product or promotion to people who aren't necessarily ready to read it.
Inbound marketing uses online content to attract its target audience (personas) to its websites, providing resources that are useful to them. A simple yet extremely valuable inbound marketing tool is a blog, which allows your site to incorporate the keywords your targeted customers are looking for.
Therefore, inbound marketing is a methodology that uses digital marketing tools to attract, convert and delight customers. Digital marketing, on the other hand, is simply a generic term to describe online marketing tactics of any kind, regardless of whether they are considered in or out.